Group #26113888 — subgroups

Subgroups — #26113888

Order 12032.

556 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252455	C₂	1	1	yes	maximal, characteristic, complemented
2	#20242123	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242056	C₂	1	2	yes	maximal, complemented
4	#20241278	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3151	C₂	1	1	yes	maximal, characteristic
6	#15689201	—	2	2	no	—
7	D₄×C₄₇⋊C₈	—	2	2	no	—
8	#15689176	C₂²	1	2	yes	—
9	#15689147	C₂²	1	2	yes	—
10	#15689090	—	2	2	no	—
11	#15688872	—	2	1	no	—
12	#15688867	—	2	2	no	—
13	#15688867	—	2	2	no	—
14	#15688867	—	2	1	no	—
15	C₂×AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
16	C₄₇×#532	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#496	C₄	1	4	yes	—
19	C₄₇×#493	—	2	1	no	—
20	C₄₇×#492	—	2	1	no	—
21	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#10625329	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
28	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
29	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
30	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
31	C₄×C₄₇⋊C₈	—	2	2	no	—
32	C₂×#41×C₄₇	D₄	1	2	yes	—
33	C₂²×D₄×C₄₇	—	2	1	no	—
34	C₂²×D₄×C₄₇	—	2	2	no	—
35	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
36	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
37	C₂×SD₁₆×C₄₇	—	2	4	no	—
38	C₂×D₈×C₄₇	—	2	4	no	—
39	C₂×M₁₆×C₄₇	—	2	1	no	—
40	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
41	#127×C₄₇	—	2	1	no	—
42	#127×C₄₇	—	2	2	no	—
43	#127×C₄₇	C₂×C₄	1	2	yes	—
44	#127×C₄₇	D₄	1	1	yes	characteristic
45	#124×C₄₇	C₂×C₄	1	2	yes	—
46	#121×C₄₇	—	2	2	no	—
47	C₄×D₄×C₄₇	—	2	2	no	—
48	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
49	#97×C₄₇	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₄₇	—	2	1	no	—
51	C₂⁴×C₄₇	—	4	1	no	—
52	#41×C₄₇	—	4	2	no	—
53	#41×C₄₇	—	4	2	no	—
54	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
55	C₂×D₄×C₄₇	—	2	2	no	—
56	C₂×D₄×C₄₇	—	2	2	no	—
57	C₂×D₄×C₄₇	—	2	4	no	—
58	C₂×D₄×C₄₇	—	2	2	no	—
59	C₂×D₄×C₄₇	—	4	2	no	—
60	C₂×D₄×C₄₇	—	4	2	no	—
61	C₂×D₄×C₄₇	—	4	1	no	—
62	C₂×D₄×C₄₇	—	4	2	no	—
63	C₂×D₄×C₄₇	—	8	2	no	—
64	C₂×D₄×C₄₇	—	8	2	no	—
65	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	#41	1	2	yes	—
69	SD₁₆×C₄₇	—	4	8	no	—
70	D₈×C₄₇	—	4	8	no	—
71	M₁₆×C₄₇	—	2	2	no	—
72	M₁₆×C₄₇	—	2	2	no	—
73	C₂×C₈×C₄₇	—	2	2	no	—
74	C₄⋊C₄×C₄₇	—	2	2	no	—
75	C₂²⋊C₄×C₄₇	—	2	4	no	—
76	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₄₇	C₂×D₄	1	2	yes	—
79	#10625329	—	8	2	no	—
80	#10625329	—	8	2	no	—
81	C₂×C₄₇⋊C₈	—	2	2	no	—
82	C₂×C₄₇⋊C₈	—	2	2	no	—
83	C₂×C₄₇⋊C₈	—	4	2	no	—
84	C₂×C₄₇⋊C₈	—	8	2	no	—
85	C₂³×C₄₇	—	2	2	no	—
86	C₂³×C₄₇	—	4	2	no	—
87	C₂³×C₄₇	—	8	2	no	—
88	C₂³×C₄₇	—	8	4	no	—
89	C₂³×C₄₇	#123	1	1	yes	characteristic
90	Q₈×C₄₇	—	4	2	no	—
91	D₄×C₄₇	—	4	2	no	—
92	D₄×C₄₇	—	4	4	no	—
93	D₄×C₄₇	—	4	2	no	—
94	D₄×C₄₇	—	4	2	no	—
95	D₄×C₄₇	—	8	4	no	—
96	D₄×C₄₇	—	8	2	no	—
97	D₄×C₄₇	—	8	1	no	—
98	D₄×C₄₇	—	8	1	no	—
99	D₄×C₄₇	—	8	2	no	—
100	D₄×C₄₇	—	8	2	no	—
101	C₂×C₄×C₄₇	—	2	1	no	—
102	C₂×C₄×C₄₇	—	2	1	no	—
103	C₂×C₄×C₄₇	—	2	2	no	—
104	C₂×C₄×C₄₇	—	2	2	no	—
105	C₂×C₄×C₄₇	—	2	2	no	—
106	C₂×C₄×C₄₇	—	4	2	no	—
107	C₂×C₄×C₄₇	—	4	2	no	—
108	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
110	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
111	C₂×C₄×C₄₇	#121	1	2	yes	—
112	C₈×C₄₇	—	2	4	no	—
113	C₄₇⋊C₈	—	4	2	no	—
114	C₄₇⋊C₈	—	4	2	no	—
115	C₄₇⋊C₈	—	8	2	no	—
116	#9437	—	47	1	no	maximal, Sylow
117	C₂²×C₄₇	—	2	1	no	—
118	C₂²×C₄₇	—	2	2	no	—
119	C₂²×C₄₇	—	4	2	no	—
120	C₂²×C₄₇	—	4	4	no	—
121	C₂²×C₄₇	—	8	2	no	—
122	C₂²×C₄₇	—	8	4	no	—
123	C₂²×C₄₇	—	16	4	no	—
124	C₂²×C₄₇	#386	1	1	yes	characteristic
125	C₄×C₄₇	—	2	1	no	—
126	C₄×C₄₇	—	2	2	no	—
127	C₄×C₄₇	—	4	2	no	—
128	C₄×C₄₇	#453	1	1	yes	characteristic
129	C₄×C₄₇	#453	1	1	yes	characteristic
130	C₄×C₄₇	#471	1	2	yes	—
131	C₄×C₄₇	#472	1	2	yes	—
132	#3151	D₄₇	1	1	yes	characteristic
133	#2979	—	47	1	no	—
134	#1560	—	47	1	no	—
135	#1545	—	47	2	no	—
136	#1299	—	47	2	no	—
137	C₂×C₄₇	—	4	1	no	—
138	C₂×C₄₇	—	8	2	no	—
139	C₂×C₄₇	—	16	2	no	—
140	C₂×C₄₇	#1887	1	1	yes	characteristic
141	C₂×C₄₇	#1907	1	2	yes	—
142	C₂×AGL(1,ℤ/8)	—	2	2	no	—
143	#532	C₂×D₄₇	1	1	yes	characteristic
144	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
145	#496	Dic₄₇	1	4	yes	—
146	#493	—	2	1	no	—
147	#492	—	2	1	no	—
148	#436	—	94	2	no	—
149	C₈×D₄	—	94	2	no	—
150	#431	—	47	2	no	—
151	#423	—	47	2	no	—
152	#408	—	94	2	no	—
153	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
154	#333	—	94	1	no	—
155	#331	—	94	2	no	—
156	#331	—	94	2	no	—
157	#331	—	94	1	no	—
158	C₄₇	#9437	1	1	yes	characteristic, complemented, Sylow
159	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
160	C₂²×D₄	—	2	2	no	—
161	C₂²×D₄	—	2	1	no	—
162	AGL(1,ℤ/8)	—	4	4	no	—
163	AGL(1,ℤ/8)	—	4	4	no	—
164	C₂×SD₁₆	—	2	4	no	—
165	C₂×D₈	—	2	4	no	—
166	C₂×M₁₆	—	2	1	no	—
167	C₂×M₁₆	—	94	2	no	—
168	C₂×M₁₆	—	94	2	no	—
169	C₂²×C₈	—	94	2	no	—
170	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
171	#127	—	2	2	no	—
172	#127	—	2	1	no	—
173	#127	C₂×Dic₄₇	1	2	yes	—
174	#127	C₂²⋊D₄₇	1	1	yes	characteristic
175	#124	C₂×Dic₄₇	1	2	yes	—
176	#121	—	2	2	no	—
177	C₄×D₄	—	2	2	no	—
178	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
179	C₄⋊C₈	—	47	2	no	—
180	C₄⋊C₈	—	47	2	no	—
181	C₄⋊C₈	—	94	2	no	—
182	C₄⋊C₈	—	94	2	no	—
183	C₂²⋊C₈	—	94	4	no	—
184	C₂²⋊C₈	—	94	2	no	—
185	#97	C₂×Dic₄₇	1	2	yes	—
186	C₄×C₈	—	2	1	no	—
187	C₄×C₈	—	94	2	no	—
188	C₂⁴	—	4	1	no	—
189	#41	—	4	2	no	—
190	#41	—	4	2	no	—
191	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
192	C₂×D₄	—	2	2	no	—
193	C₂×D₄	—	2	2	no	—
194	C₂×D₄	—	2	4	no	—
195	C₂×D₄	—	2	2	no	—
196	C₂×D₄	—	4	2	no	—
197	C₂×D₄	—	4	2	no	—
198	C₂×D₄	—	4	1	no	—
199	C₂×D₄	—	4	2	no	—
200	C₂×D₄	—	8	2	no	—
201	C₂×D₄	—	8	2	no	—
202	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
203	C₂²×C₄	—	2	2	no	—
204	C₂²×C₄	#10625352	1	2	yes	—
205	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
206	SD₁₆	—	4	8	no	—
207	D₈	—	4	8	no	—
208	M₁₆	—	2	2	no	—
209	M₁₆	—	2	2	no	—
210	M₁₆	—	376	2	no	—
211	M₁₆	—	376	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	94	2	no	—
214	C₂×C₈	—	94	2	no	—
215	C₂×C₈	—	376	2	no	—
216	C₂×C₈	—	188	2	no	—
217	C₄⋊C₄	—	2	2	no	—
218	C₂²⋊C₄	—	2	4	no	—
219	C₄²	D₄×D₄₇	1	2	yes	—
220	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
221	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
222	C₂³	—	2	2	no	—
223	C₂³	—	4	2	no	—
224	C₂³	—	8	2	no	—
225	C₂³	—	8	4	no	—
226	C₂³	#13094005	1	1	yes	characteristic
227	Q₈	—	4	2	no	—
228	D₄	—	4	2	no	—
229	D₄	—	4	4	no	—
230	D₄	—	4	2	no	—
231	D₄	—	4	2	no	—
232	D₄	—	8	4	no	—
233	D₄	—	8	2	no	—
234	D₄	—	8	1	no	—
235	D₄	—	8	1	no	—
236	D₄	—	8	2	no	—
237	D₄	—	8	2	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	2	no	—
245	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
246	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
247	C₂×C₄	#13093992	1	1	yes	characteristic
248	C₂×C₄	#13093996	1	2	yes	—
249	C₈	—	2	4	no	—
250	C₈	—	376	2	no	—
251	C₈	—	188	2	no	—
252	C₈	—	188	2	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	4	2	no	—
256	C₂²	—	4	4	no	—
257	C₂²	—	8	2	no	—
258	C₂²	—	8	4	no	—
259	C₂²	—	16	4	no	—
260	C₂²	#15689003	1	1	yes	characteristic
261	C₄	—	2	1	no	—
262	C₄	—	2	2	no	—
263	C₄	—	4	2	no	—
264	C₄	#15689290	1	1	yes	characteristic
265	C₄	#15689290	1	1	yes	characteristic
266	C₄	#15689384	1	2	yes	—
267	C₄	#15689391	1	2	yes	—
268	C₂	—	4	1	no	—
269	C₂	—	8	2	no	—
270	C₂	—	16	2	no	—
271	C₂	#20243787	1	1	yes	characteristic
272	C₂	#20243898	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20252455

C₂

yes

maximal, characteristic, complemented

#20242123

C₂

yes

maximal, characteristic, complemented

#20242056

C₂

yes

maximal, complemented

#20241278

C₂

yes

maximal, complemented

C₄₇×#3151

C₂

yes

maximal, characteristic

#15689201

—

D₄×C₄₇⋊C₈

—

#15689176

C₂²

yes

—

#15689147

C₂²

yes

—

—

—

—

—

—

C₂×AGL(1,ℤ/8)×C₄₇

—

C₄₇×#532

C₂²

yes

characteristic

C₂×#127×C₄₇

C₂²

yes

characteristic

C₄₇×#496

C₄

yes

—

C₄₇×#493

—

C₄₇×#492

—

C₄×M₁₆×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₂×#41×C₄₇

D₄

yes

—

C₂²×D₄×C₄₇

—

C₂²×D₄×C₄₇

—

AGL(1,ℤ/8)×C₄₇

—

AGL(1,ℤ/8)×C₄₇

—

C₂×SD₁₆×C₄₇

—

C₂×D₈×C₄₇

—

C₂×M₁₆×C₄₇

—

C₄⋊Q₈×C₄₇

D₄

yes

characteristic

#127×C₄₇

—

#127×C₄₇

—

#127×C₄₇

C₂×C₄

yes

—

#127×C₄₇

D₄

yes

characteristic

#124×C₄₇

C₂×C₄

yes

—

#121×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#97×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

—

C₂⁴×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

—

SD₁₆×C₄₇

—

D₈×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

#123

yes

characteristic

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

100

D₄×C₄₇

—

101

C₂×C₄×C₄₇

—

102

C₂×C₄×C₄₇

—

103

C₂×C₄×C₄₇

—

104

C₂×C₄×C₄₇

—

105

C₂×C₄×C₄₇

—

106

C₂×C₄×C₄₇

—

107

C₂×C₄×C₄₇

—

108

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

109

C₂×C₄×C₄₇

C₄×D₄

yes

—

110

C₂×C₄×C₄₇

#120

yes

characteristic

111

C₂×C₄×C₄₇

#121

yes

—

112

C₈×C₄₇

—

113

C₄₇⋊C₈

—

114

C₄₇⋊C₈

—

115

C₄₇⋊C₈

—

116

#9437

—

maximal, Sylow

117

C₂²×C₄₇

—

118

C₂²×C₄₇

—

119

C₂²×C₄₇

—

120

C₂²×C₄₇

—

121

C₂²×C₄₇

—

122

C₂²×C₄₇

—

123

C₂²×C₄₇

—

124

C₂²×C₄₇

#386

yes

characteristic

125

C₄×C₄₇

—

126

C₄×C₄₇

—

127

C₄×C₄₇

—

128

C₄×C₄₇

#453

yes

characteristic

129

C₄×C₄₇

#453

yes

characteristic

130

C₄×C₄₇

#471

yes

—

131

C₄×C₄₇

#472

yes

—

132

#3151

D₄₇

yes

characteristic

133

#2979

—

134

#1560

—

135

#1545

—

136

#1299

—

137

C₂×C₄₇

—

138

C₂×C₄₇

—

139

C₂×C₄₇

—

140

C₂×C₄₇

#1887

yes

characteristic

141

C₂×C₄₇

#1907

yes

—

142

C₂×AGL(1,ℤ/8)

—

143

#532

C₂×D₄₇

yes

characteristic

144

C₂×#127

C₂×D₄₇

yes

characteristic

145

#496

Dic₄₇

yes

—

146

#493

—

147

#492

—

148

#436

—

149

C₈×D₄

—

150

#431

—

151

#423

—

152

#408

—

153

C₄×M₁₆

C₂×D₄₇

yes

characteristic

154

#333

—

155

#331

—

156

#331

—

157

#331

—

158

C₄₇

#9437

yes

characteristic, complemented, Sylow

159

C₂×#41

C₂²⋊D₄₇

yes

—

160

C₂²×D₄

—

161

C₂²×D₄

—

162

AGL(1,ℤ/8)

—

163

AGL(1,ℤ/8)

—

164

C₂×SD₁₆

—

165

C₂×D₈

—

166

C₂×M₁₆

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

169

C₂²×C₈

—

170

C₄⋊Q₈

C₂²⋊D₄₇

yes

characteristic

171

#127

—

172

#127

—

173

#127

C₂×Dic₄₇

yes

—

174

#127

C₂²⋊D₄₇

yes

characteristic

175

#124

C₂×Dic₄₇

yes

—

176

#121

—

177

C₄×D₄

—

178

C₂×C₄²

C₂²×D₄₇

yes

characteristic

179

C₄⋊C₈

—

180

C₄⋊C₈

—

181

C₄⋊C₈

—

182

C₄⋊C₈

—

183

C₂²⋊C₈

—

184

C₂²⋊C₈

—

185

#97

C₂×Dic₄₇

yes

—

186

C₄×C₈

—

187

C₄×C₈

—

188

C₂⁴

—

189

#41

—

190

#41

—

191

C₂×Q₈

C₂²⋊Dic₄₇

yes

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

—

196

C₂×D₄

—

197

C₂×D₄

—

198

C₂×D₄

—

199

C₂×D₄

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂×D₄

C₂²⋊Dic₄₇

yes

—

203

C₂²×C₄

—

204

C₂²×C₄

#10625352

yes

—

205

C₂²×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

206

SD₁₆

—

207

D₈

—

208

M₁₆

—

209

M₁₆

—

210

M₁₆

—

376

—

211

M₁₆

—

376

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

376

—

216

C₂×C₈

—

188

—

217

C₄⋊C₄

—

218

C₂²⋊C₄

—

219

C₄²

D₄×D₄₇

yes

—

220

C₄²

C₂²×Dic₄₇

yes

characteristic

221

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

#13094005

yes

characteristic

227

Q₈

—

228

D₄

—

229

D₄

—

230

D₄

—

231

D₄

—

232

D₄

—

233

D₄

—

234

D₄

—

235

D₄

—

236

D₄

—

237

D₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

C₂×C₂²⋊Dic₄₇

yes

characteristic

246

C₂×C₄

D₄×Dic₄₇

yes

—

247

C₂×C₄

#13093992

yes

characteristic

248

C₂×C₄

#13093996

yes

—

249

C₈

—

250

C₈

—

376

—

251

C₈

—

188

—

252

C₈

—

188

—

253

C₂²

—

254

C₂²

—

255

C₂²

—

256

C₂²

—

257

C₂²

—

258

C₂²

—

259

C₂²

—

260

C₂²

#15689003

yes

characteristic

261

C₄

—

262

C₄

—

263

C₄

—

264

C₄

#15689290

yes

characteristic

265

C₄

#15689290

yes

characteristic

266

C₄

#15689384

yes

—

267

C₄

#15689391

yes

—

268

C₂

—

269

C₂

—

270

C₂

—

271

C₂

#20243787

yes

characteristic

272

C₂

#20243898

yes

—

	subgroup	G/H
center	C₂²	#15689003
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting, prime radical	C₄₇×#3151	C₂
socle	C₂²×C₄₇	#386
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#3151	D₄₇
hypocenter	C₄₇	#9437
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3151

subgroup

G/H

center

C₂²

#15689003

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting, prime radical

C₄₇×#3151

C₂

socle

C₂²×C₄₇

#386

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3151

N	H ≅ G/N	type
1. #20252455	C₂	semidirect
2. #20242123	C₂	semidirect
3. #20242056	C₂	semidirect
4. #20241278	C₂	semidirect
158. C₄₇	#9437	semidirect

H ≅ G/N

type

1. #20252455

C₂

semidirect

2. #20242123

C₂

semidirect

3. #20242056

C₂

semidirect

4. #20241278

C₂

semidirect

158. C₄₇

#9437

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20252455	2
#20242123	2
#20242056	2
#20241278	2
C₄₇×#3151	2
#9437	47

subgroup

index

C₄₇×#3151

Subgroups — #26113888

Conjugacy classes of subgroups

Complements

Maximal subgroups